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Scholars' Mine Masters Theses
Student Research & Creative Works
Fall 2014
Hedge fund replication using a strategy specific modeling approach Sujit Subhash
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HEDGE FUND REPLICATION USING A STRATEGY SPECIFIC MODELING APPROACH
By
SUJIT SUBHASH
A THESIS Presented to the Faculty of the Graduate School of the MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY In Partial Fulfillment of the Requirements for the Degree
MASTER OF SCIENCE IN ENGINEERING MANAGEMENT 2014 Approved by
Dr. David Enke, Advisor Dr. Cihan Dagli Dr. Ruwen Qin
2014 Sujit Subhash All Rights Reserved
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PUBLICATION THESIS OPTION
This thesis consists of the following two papers that have been prepared in the styles specified by the Industrial and Systems Engineering Research Conference and the Journal of Asset Management, respectively: Pages 4-21 were accepted and published in the proceedings of the 2014 Industrial and Systems Engineering Research Conference under the title of “Hedge Fund Replication using Liquid ETFs and Regression Analysis”. Pages 22-59 are intended for submission to the Journal of Asset Management under the title of “Hedge Fund Replication using Strategy Specific Factors”.
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ABSTRACT
Institutional investors and wealthy individuals have in the past allocated a significant portion of their portfolios to hedge funds with the expectation of unconditional and uncorrelated returns to the market. However, the financial crisis of 2008 has heightened investor sensitivity to the high fees, illiquidity, and lockup periods typically associated with hedge funds. Hedge fund indexes showing excellent returns and low volatility contain funds that are closed to new investments, while the performance of investable funds have been shown to be inferior to their non-investable counterparts. The lack of transparency and extreme variation in the performance of hedge funds make the due diligence process critical in selecting the right fund. These challenges have motivated a search for an alternative to hedge funds. Recent research has established that a significant part of hedge fund returns can be replicated by portfolios constructed using liquid financial instruments. Hedge fund replication products, or clones, answer several challenges faced by hedge fund investors by providing daily liquidity, easy monitoring, and complete transparency at a significant cost advantage to hedge funds. This thesis examines the performance of clones constructed with factors selected based on the economic relevance to each hedge fund strategy by using both a passive model with constant portfolio weights, and an active model requiring monthly rebalancing of portfolio weights. These clones are further compared against the top performing hedge funds to analyze if the clones continue to deliver against a higher benchmark with regard to both risk and return.
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ACKNOWLEDGMENTS
I am extremely indebted to my advisor Dr. David Enke for giving me the opportunity to pursue my master’s degree under his guidance. His passion for the field of finance and interest in hedge funds were instrumental in shaping my own. For this I am forever grateful. This thesis and my Master’s degree would not have been possible without the patience and trust he showed in supporting my research. I am thankful to Dr. Cihan Dagli and Dr. Ruwen Qin for bringing their vast experience and knowledge to my advisory committee and for guiding me through the challenges I faced in my research. I would like to thank Mohamed Milad for all the help he provided me in understanding regression models, and for taking the time to clear my doubts. I take this opportunity to acknowledge the encouragement provided by all my cousins, especially Vivek Anand, James Jimmy, and Alex Jimmy. I would especially like to thank Tejaswi Materla. Her limitless support and motivation brought the best out of me. Most importantly, I thank my parents for their prayers and blessings, and for always believing in me. My brother and sister have always given me their unequivocal support and I will always remember how that got me through the tough days. My father Dr. Subhash Jacob has been my inspiration and above all I hope I made him proud.
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TABLE OF CONTENTS
Page PUBLICATION THESIS OPTION...................................................................................iii ABSTRACT.......................................................................................................................iv ACKNOWLEDGEMENTS ................................................................................................v LIST OF TABLES..............................................................................................................ix SECTION 1. INTRODUCTION.............................................................................................1 PAPER I.
Hedge Fund Replication using Liquid ETFs and Regression Analysis……………………………………………….........................4 Abstract………………………………………………………………....................4 1. Introduction..........................................................................................................6 2. Methodology........................................................................................................7 3. Initial Modeling and Results................................................................................8 3.1. Fixed-Weight Clones............................................................................8 3.2. Rolling Window Clones......................................................................11 4. New Data Selection and Results........................................................................13 4.1. The Top Sharpe Ratio Funds and Their Clones..................................13 4.2. The Top Return Funds and Their Clones............................................16
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5. Conclusion.........................................................................................................19 References.............................................................................................................20 II.
Hedge Fund Replication using Strategy Specific Factors......................................22 Abstract..................................................................................................................22 1. Introduction......................................................................................................24 2.
Methodology...................................................................................................27 2.1. Initial motivation.................................................................................28 2.2. Modeling approach.............................................................................30
3. Strategy Overview..........................................................................................31 3.1. Convertible Arbitrage.........................................................................31 3.2. Dedicated Short Bias..........................................................................32 3.3. Emerging Market................................................................................33 3.4. Equity Market Neutral........................................................................34 3.5. Event Driven.......................................................................................35 3.6. Fixed Income Arbitrage......................................................................35 3.7. Global Macro......................................................................................37 3.8. Long/Short Equity...............................................................................38 3.9. Managed Futures.................................................................................39 3.10. Multi-Strategy...................................................................................40 3.11. Fund-of-Funds..................................................................................41 4. Results......…………………………………………………………................42 4.1. All Funds………………………………………………….................42 4.2. Top 50% Sharpe Ratio......…………………………………..............47
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4.3. Top 50% Returns…………………………………………................50 5. Conclusion....................………………………………………………….......54 References………………………………………………………........................56 SECTION 2. CONCLUSION ………………………………………………………….........60 VITA………………………………………………………………………………..........62
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LIST OF TABLES Table
Page
PAPER I 1. Comparison of all funds and their fixed weight clones.........................................10 2. Comparison of all funds and their 24-month rolling window clones....................12 3. Comparison of top 50% Sharpe ratio funds and their fixed-weight clones...........14 4. Comparison of top 50% Sharpe ratio funds and their 24-month rolling window clone.........................................................................................................15 5. Comparison of top 50% average return funds and their fixed-weight clones........17 6. Comparison of top 50% average return funds and their 24-month rolling window clones………….......................................................................................18
PAPER II 1. Performance comparison for fixed weight model for all funds and their clones.....................................................................................................................45 2. Performance comparison for rolling window model for all funds and their clones.............................................................................................................46 3. Performance comparison for fixed weight model for top 50% Sharpe ratio funds and their clones……………………………………....................................48 4. Performance comparison for rolling window model for top 50% Sharpe ratio funds and their clones……………………………………............…………49 5. Performance comparison for fixed weight model for top 50% return funds and their clones…………………………………………………………..............51 6. Performance comparison for rolling window model for top 50% Sharpe ratio funds and their clones………………………………………………........…53
1. INTRODUCTION
Hedge funds have traditionally served exclusively to wealthy individuals and institutional investors with the promise of delivering uncorrelated returns, absolute positive returns irrespective of market direction, and protecting investor capital. However, the financial crisis of 2008 has forced many investors to take a more critical look at hedge funds. Hedge funds charge very high fees in terms of management and performance fees, often have lockup periods, and offer very little or no transparency. The opaque nature of the hedge fund industry also makes it challenging to select hedge funds to invest in. Fund-of-funds hedge funds have traditionally answered this due diligence requirement at the price of an additional layer of fees, however, fund-of-funds again differ in their ability to add value and selecting an appropriate fund-of-funds can be just as challenging. Hedge fund indexes showing excellent return and low volatility are constructed using funds that choose to voluntarily report their data and have several biases associated with them that overestimate their returns. These indexes are also not truly representable of the investable hedge fund universe as they also contain funds that are closed to new investments. Hedge fund replication products, or clones, address several of the challenges faced by investors considering investments in hedge funds. Hedge fund clones offer daily liquidity, complete transparency, and scalability to large investments, and also provide investors with immediate exposure to a desired hedge fund strategy. Clones can be used in their portfolios in lieu of hedge funds or during the due diligence period until they find
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a suitable hedge fund manager to invest in so as to not miss immediate opportunities. The cost advantage over hedge fund investing and ease of monitoring of clones have made them a practical substitute to hedge funds in the portfolios of institutional and sophisticated investors. These replication products also clear the accessibility hurdle to investors who fail to meet the accreditation and minimum investment requirements of hedge funds, thereby allowing even the average retail trader access to hedge fund like returns and diversification options. Paper 1 presents the idea of using funds selected based on performance characteristics to model clones, offering clones that are targeted to capture those characteristics in their performance. A general set of factors representing basic sources of risk covering stocks, bonds, currency, credit, and commodities are used to construct the clones. Both fixed weight and rolling window models, each offering different benefits and serving different investor needs, are used in modeling the clones for each hedge fund strategy. The clones are constructed for three sets of data, including all the funds, the funds with top 50% Sharpe ratios, and the top 50% returns through the sample period. Paper 2 goes beyond the standard five factors used in paper 1 and progresses to using factors that are specifically chosen according to the underlying hedge fund strategy. The performances of the clones from these factors are compared to the performance of the funds and the clones made from the five basic factors that are used in paper 1. The fixed weight and rolling window models are again used to develop the clones. The clones constructed from factors specific to each hedge fund are again compared against the top performing funds to analyze if these clones continue to deliver better performance against a higher benchmark.
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This thesis examines the importance of selecting factors that are economically relevant to each hedge fund strategy and seeks to validate the well-established consensus that investors can obtain hedge fund like returns without the difficulties associated with investing in a standard hedge fund.
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PAPER
I. Hedge Fund Replication using Liquid ETFs and Regression Analysis
Sujit Subhash and David Enke Engineering Management and Systems Engineering Missouri University of Science and Technology Rolla, Missouri, 65409-0370, USA
Abstract
Hedge fund replication involves the use of common factors or liquid Exchange Traded Funds (ETFs) in order to replicate the risk-return profile of common hedge fund strategies, including Convertible Arbitrage, Long/Short Equity, Global Marco, and Event Driven, among others. The benefits of replication are that traders and risk managers can replicate the risk-return profile of various hedge fund strategies or portfolios with increased transparency and lower costs, including lower management and performance fees. The added liquidity of ETFs also allow traders to avoid common hedge fund lockup periods. To model various hedge fund strategies, the authors utilize historical hedge fund return data, along with regression analysis to model the returns of common trading and hedging strategies. Various input data selection procedures, such as those focusing on the best returns in each strategy category, or using the individual funds with the highest
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Sharpe ratios, are also tested to determine their impact on the replication performance, as well as the risk-return flexibility of the replication modeling. Keywords Hedge Fund Replication, Exchange Traded Funds, Regression, Financial Risk and Return
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1. Introduction
Hedge funds cater to wealthy, accredited investors. As a result, it is not uncommon for hedge funds to charge a management fee of 1-2% of assets, in addition to a performance fee of 10-20% [1]. In view of recent economic events, investors have grown increasingly nervous over these hefty fees along with other restrictions, such as lockup periods, lack of transparency, illiquidity and the extensive due diligence that are associated with hedge funds. Broad based hedge fund index replication products, such as the Goldman Sachs Absolute Return Tracker Index [2] and the Merrill Lynch Factor Index [3], are already being offered to institutional investors, with Credit Swiss now offering replicators for both the overall hedge fund industry and individual hedge fund strategies [4]. Imitation funds, such as Global X Guru Index and Alpha Clone Alternative Alpha that invest directly into long positions observed from the 13F filings of top fund managers, are also in existence. However, this group of replicators is secretive of their methods and typically charge high fees [5].
Investors have long tried to understand the source of returns of top performing investment institutions and managers, and have been ready to pay a premium for returns that outperform the market. Sharpe [6] provided a method to benchmark mutual fund performance and explains their return in terms of various asset classes. This paved the way to extend style analysis to hedge funds for estimating their risk exposures. Fung and Hsieh [7] used principle component analysis to group funds based on both their correlations with each other and their relation to various styles. Fung and Hsieh [8]
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showed that trend following styles can be replicated to a fair degree by using look-back options.
A paper by Hasanhodzic and Lo [9] showed that for certain hedge fund categories it was possible to obtain comparable performance using a linear factor model that has a simple economic interpretation. This work will be the focus of our research as we use a similar factor model to test the performance of the clones using various strategies. One goal of the modeling is to maintain the simplicity of the linear factor model so as to be both attractive and accessible to a typical investor, while now allowing for added risk-return flexibility.
In the following sections we discuss our research methodology and then elaborate on the cloning techniques used in Hasanhodzic and Lo [9]. These techniques include fixed weight clones for a passive investor, along with a rolling window clone for an investor who prefers monthly rebalancing. We then use two techniques for satisfying different investor preferences. To obtain a more balanced risk-reward ratio, we use the funds with the highest Sharpe ratio in the cloning process. For those willing to take more risk, we focus on cloning the funds with the best returns. We discuss the impact of this selection process on the replication performance results and conclude with suggestions for further improvement and added flexibility in the clones.
2. Methodology
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For our research methodology we use a sample of 1495 hedge funds with monthly returns from August 1996 to September 2008. The hedge funds are classified into eleven fund categories, including Event Driven, Long/Short Equity Hedge, Managed Futures, Global Macro, Fixed Income Arbitrage, Emerging Markets, Convertible Arbitrage, Dedicated Short-Bias, Multi-Strategy, Equity Market Neutral and Fund-of-Funds.
Hasanhodzic and Lo [9] showed that portfolios made up of common risk factors can provide comparable performance to a number of hedge fund categories and have the benefit of being transparent and easily traded through liquid instruments, such as Exchange Traded Funds (ETFs). The factors used by Hasanhodzic and Lo [9] include: 1) USD: U.S. Dollar Index Return; 2) SP500: S&P 500 Total Return; 3) Credit: the spread between the Lehman Corporate Bond Index and the Lehman Treasury Index; 4) Bond: Lehman Corporate AA Intermediate Bond Index; and 5) GSCI: Goldman Sachs Commodity Index Total Return. These factors are used to run a constrained regression on hedge funds in each fund category to obtain portfolio weights of the risk factors in the clones. Section 3 provides more details on the modeling approach used by Hasanhodzic and Lo [9] in constructing their fixed-weight and rolling window clones.
3. Initial Modeling and Results 3.1 Fixed-Weight Clones
To construct the fixed weight clones, we run a regression on the fund’s returns (Rit) with the aforementioned five factors. During modeling, the regression coefficients are constrained to sum to one, while also dropping the intercept. Dropping the intercept
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forces the least-squares algorithm to use the factor means to fit the mean return of the fund [9]. The beta coefficients can be interpreted as portfolio weights in the clone.
Rit = βi1USDt + βi2Bondt + βi3Creditt +βi4SP500t +βi5GSCIt + Ԑit,
(1)
t = 1, 2…T, subject to βi1+…. +βi5 = 1
The estimated regression coefficients are used as the portfolio weights to give the portfolio returns (R*it), which are then renormalized to obtain the clone portfolio return (Ritclone) that has the same sample volatility as the original fund [9].
R*it = β*i1USDt + β*i2Bondt + β*i3Creditt +β*i4SP500t +β*i5GSCIt
Ritclone = γi R*it,
γi = σR/ σR*
(2)
(3)
The portfolio weights and renormalization factors of the fixed-weight clones stay constant over time for each clone. Table 1 presents a comparison of the performance of the fixed-weight clones, as well as the funds from which they are derived.
The average mean return of the clones are higher than that of the funds in the cases of Equity Market Neutral, Managed Futures and Global Macro. It must be noted that the clone portfolios are less expensive and are considerably more liquid than their fund counterparts, and hence deserve consideration even in categories where they slightly underperform.
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Table 1: Comparison of all funds and their fixed weight clones Categories
Sample Size
Annual Mean Return % Mean
Annual SD % SD
Mean
SD
Annual Sharpe Mean
SD
Fixed Weight Funds Convertible Arbitrage
53
8.6386
3.7167
6.3012
4.7895
2.328
3.2404
Dedicated Short Bias
13
4.8201
5.4648
23.1809
8.6865
0.1837
0.2631
Emerging Markets
67
16.7964
7.9913
18.7842
11.8901
1.2251
0.9862
Equity Market Neutral
76
7.6546
4.3231
9.146
9.6008
1.4457
1.3988
Event Driven
59
10.6814
5.4156
8.5589
4.2339
1.4374
0.7565
Fixed Income Arbitrage
42
8.5226
2.792
6.6932
4.1345
2.1373
2.5498
Global Macro
62
13.3915
6.8244
15.0045
7.7812
0.9909
0.4618
Long/Short Equity Hedge
498
12.3541
6.6903
14.4087
7.9523
0.966
0.4416
Managed Futures
211
13.5724
7.6039
18.8518
10.2627
0.789
0.3774
Multi-Strategy
91
9.3471
5.7469
9.4222
7.3416
1.3492
0.8466
Fund-of-Funds
323
9.129
2.996
7.6545
4.839
1.4718
0.6511
Total
1495 Fixed Weight Linear Clones
Convertible Arbitrage
53
4.7008
3.2187
6.3012
4.7895
1.0261
0.455
Dedicated Short Bias
13
8.0536
9.2329
23.1809
8.6865
0.3734
0.3749
Emerging Markets
67
9.3651
4.9013
18.7842
11.8901
0.6733
0.4244
Equity Market Neutral
76
9.4393
10.406
9.146
9.6008
1.1232
0.3931
Event Driven
59
6.3965
3.0841
8.5589
4.2339
0.844
0.3597
Fixed Income Arbitrage
42
6.6233
3.4836
6.6932
4.1345
1.1654
0.447
Global Macro
62
13.8627
10.1455
15.0045
7.7812
0.9978
0.4821
Long/Short Equity Hedge
498
8.1456
6.8011
14.4087
7.9523
0.6458
0.4134
Managed Futures
211
22.1205
12.4523
18.8518
10.2627
1.2398
0.4036
Multi-Strategy
91
6.8146
7.9215
9.4222
7.3416
0.9307
0.5266
Fund-of-Funds
323
6.7619
3.2923
7.6545
4.839
1.0501
0.4075
Total
1495
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3.2 Rolling Window Clones
We apply a similar process to construct the rolling-window clones, but now a 24-month rolling window regression is used to estimate the portfolio weights of the risk factors, with rebalancing each month for every clone [9].
Rit-k = βit1USDt-k + βit2Bondt-k + βit3Creditt-k +βit4SP500t-k +βit5GSCIt-k + Ԑit-k,
(4)
k = 1 to 24, subject to βit1+…. +βit5 = 1
With the renormalization now computed within the rolling window, the volatility of each clone will no longer be the same as the corresponding fund. Nonetheless, as long as the volatiles of the funds do not drastically shift over time, the clones and funds will still have similar volatilities [9].
R*it = β*it1USDt + β*it2Bondt + β*it3Creditt +β*it4SP500t +β*it5GSCIt
Ritclone = γit R*it,
γit =
2 √∑24 𝑘=1(𝑅𝑖𝑡−𝑘 −𝜇𝑅𝑖𝑡 ) ∗ 2 √∑24 𝑘=1(𝑅𝑖𝑡−𝑘 −𝜇𝑅∗𝑖𝑡 )
(5)
(6)
Table 2 contains a performance comparison of rolling window clones and funds from which they are derived.
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Table 2: Comparison of all funds and their 24-month rolling window clones Categories
Sample Size
Annual Mean Return %
Annual SD %
Annual Sharpe
Mean
Mean
SD
Mean
SD
SD
Rolling Window Funds Convertible Arbitrage
53
7.6507
3.9782
4.6442
4.3293
3.065
5.0339
Dedicated Short Bias
13
3.3783
5.3497
19.1765
8.6665
0.146
0.3303
Emerging Markets
67
16.1654
8.0069
14.2624
10.6382
1.6375
1.2125
Equity Market Neutral
76
6.1055
4.3357
6.3047
5.9482
1.8797
2.9815
Event Driven
59
9.6585
4.769
6.1441
3.5295
1.8072
0.858
Fixed Income Arbitrage
42
7.0253
2.2164
4.4676
3.0117
2.9832
4.4232
Global Macro
62
10.9135
5.3513
11.5579
6.1696
1.0883
0.5219
Long/Short Equity Hedge
498
10.7916
6.238
10.4254
6.5072
1.1911
0.5168
Managed Futures
211
10.7406
6.1403
15.2862
9.0307
0.8118
0.475
Multi-Strategy
91
8.3995
4.3511
6.2706
4.5067
1.6832
0.9916
Fund-of-Funds
323
8.8644
2.9278
6.2418
4.1473
1.7947
0.8362
Total
1495 Rolling Window Linear Clones
Convertible Arbitrage
53
2.4477
4.2366
5.6583
4.5354
0.5935
0.5825
Dedicated Short Bias
13
-1.0536
5.991
15.9331
6.4144
-0.1605
0.4692
Emerging Markets
67
9.5284
9.1957
14.642
8.8071
0.728
0.4031
Equity Market Neutral
76
4.1527
5.2352
7.201
6.5294
0.6519
0.5498
Event Driven
59
5.8614
4.5821
7.7538
4.3007
0.8631
0.5219
Fixed Income Arbitrage
42
3.04
3.4865
5.0277
3.4534
0.7925
0.4946
Global Macro
62
9.0461
10.9186
13.5485
7.5443
0.685
0.6525
Long/Short Equity Hedge
498
9.942
8.4005
12.4677
6.7452
0.8347
0.4738
Managed Futures
211
16.0113
13.3889
17.7766
10.7423
0.9203
0.4899
Multi-Strategy
91
4.0189
8.5099
8.3197
6.3314
0.7718
0.6655
Fund-of-Funds
323
5.1649
3.3946
5.8286
4.1919
0.9629
0.2869
Total
1495
The rolling window clones offer comparable performance in the fund categories of Global Macro, Long/Short Equity Hedge and Managed Futures. Our analysis was fairly consistent with the results obtained in Hasanhodzic and Lo [9], with exception in the category of Convertible Arbitrage. In section 4 we focus on
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improving the performance and flexibility of the replicating model by using funds with higher performance in terms of Sharpe ratio and returns. We test to see if setting a higher benchmark for the replication procedure will continue to produce good clones, even though less data is used, and whether isolating risk and/or return can provide more options for individual investors.
4. New Data Selection and Results
We identified and tested two data selection strategies to improve the risk-to-return flexibility of the clones. By focusing on the funds with higher Sharpe ratios, we obtain clone portfolios with improved risk-to-return ratios as compared to clones from all the funds in each category. Likewise, replicating the funds with higher return results in clones with higher average returns. Although this approach uses less data and may involve accepting more risk, these clones should provide improved Sharpe ratios as compared to cloning all funds. For the modeling, we use the same fixed-weight and rolling window approach of Hasanhodzic and Lo [9], as highlighted in section 3.
4.1 The Top Sharpe Ratio Funds and Their Clones
Table 3 gives the performance comparison of the fixed weight funds with the highest Sharpe ratios, along with their clones. As expected, in comparing the results in Table 3 with Table 1, we see that on average the clones in Table 3 have higher Sharpe ratios across all fund categories, and in cases of Dedicated Short Bias (13.35% with clones of
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selected funds vs. 8.05% with clones of all funds), Long/Short (9.26% with clones of selected funds vs. 8.15% with clones of all funds) and Emerging Markets (10% with clones of selected funds vs. 9.37% with clones of all funds), the clones also have higher expected returns. Of note is the significant reduction of standard-deviation in average expected returns of clones in the cases of Global Macro (6.3% with clones of selected funds vs. 10.14% with clones of all funds), Equity Market Neutral (3.3% with clones of selected funds vs. 10.41% with clones of all funds) and Multi-Strategy (4.18% with clones of selected funds vs. 7.92% with clones of all funds).
Table 3: Comparison of top 50% Sharpe ratio funds and their fixed-weight clones Sample Size
Categories
Annual Mean Return % Mean
Annual SD % SD
Mean
SD
Annual Sharpe Mean
SD
Fixed Weight Funds using the Top 50% Sharpe Ratios Convertible Arbitrage
26
9.5625
3.5997
4.1298
2.1341
3.6774
4.2419
Dedicated Short Bias
6
9.5046
3.9039
24.2565
8.161
0.4121
0.1469
Emerging Markets
33
17.9815
6.9874
13.0869
8.5666
1.8165
1.1225
Equity Market Neutral
38
8.8922
3.7544
4.9206
2.4066
2.3083
1.542
Event Driven
29
11.4844
5.5873
6.5063
3.5807
1.9462
0.7286
Fixed Income Arbitrage
21
8.9258
2.6578
3.7946
1.7327
3.3749
3.1704
Global Macro
31
15.5062
6.8798
12.1624
6.5032
1.3462
0.3656
Long/Short Equity Hedge
249
13.8479
6.8535
11.1263
5.704
1.296
0.3463
Managed Futures
105
15.1096
7.4624
15.6007
8.2941
1.0414
0.3662
Multi-Strategy
45
10.7685
4.7328
5.5951
2.7972
2.0296
0.5772
Fund-of-Funds
161
9.1174
2.6564
4.8578
1.8484
1.9809
0.5022
Total
744 Fixed Weight Linear Clones with the Top 50% Sharpe Ratios
Convertible Arbitrage
26
4.6769
2.0452
4.1298
2.1341
1.2509
0.3082
Dedicated Short Bias
6
13.3449
11.6547
24.2565
8.161
0.5965
0.4579
Emerging Markets
33
9.9984
4.6832
13.0869
8.5666
0.9522
0.4054
Equity Market Neutral
38
6.0046
3.2998
4.9206
2.4066
1.2558
0.3239
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Table 3: Comparison of top 50% Sharpe ratio funds and their fixed-weight clones (cont.) Event Driven
29
6.0871
2.6332
6.5063
3.5807
1.037
0.3429
Fixed Income Arbitrage
21
5.6505
2.9976
3.7946
1.7327
1.4688
0.2791
Global Macro
31
11.7792
6.3004
12.1624
6.5032
1.0176
0.374
Long/Short Equity Hedge
249
9.2642
6.9928
11.1263
5.704
0.8492
0.3628
Managed Futures
105
18.6596
11.3459
15.6007
8.2941
1.2719
0.4328
Multi -Strategy
45
6.4932
4.1814
5.5951
2.7972
1.1767
0.3128
Fund-of-Funds
161
6.2013
2.9396
4.8578
1.8484
1.2758
0.2604
Total
744
Table 4 represents the rolling window clones with the same strategy of using the funds with the highest Sharpe ratios. Comparing Table 4 with Table 2 shows that this strategy improves the average Sharpe ratio of clones across all fund categories, and therefore can be used even with an active portfolio rebalancing approach to obtain a desired risk-toreward ratio.
Table 4: Comparison of top 50% Sharpe ratio funds and their 24-month rolling window clones Sample Size
Categories
Annual Mean Return % Mean
Annual SD % SD
Mean
SD
Annual Sharpe Mean
SD
Rolling Window Funds using Top 50% Sharpe Ratios Convertible Arbitrage
26
8.2385
3.1204
3.0062
1.5436
4.9181
6.7423
Dedicated Short Bias
6
7.6179
4.8209
20.4851
8.052
0.3991
0.2751
Emerging Markets
33
15.6074
6.8253
8.8609
6.6448
2.3523
1.3586
Equity Market Neutral
38
7.2812
4.0085
3.4608
1.8132
3.0936
3.8545
Event Driven
29
9.9237
4.7103
4.6715
2.8791
2.3656
0.8355
Fixed Income Arbitrage
21
6.9905
2.0902
2.3775
1.1976
4.8203
5.7388
Global Macro
31
12.1548
5.7268
8.8463
5.1092
1.4771
0.427
Long/Short Equity Hedge
249
11.4931
6.5157
7.8833
4.6788
1.5402
0.4282
Managed Futures
105
11.839
5.8608
12.1286
7.1692
1.1036
0.5057
Multi-Strategy
45
9.4822
3.6039
4.1958
2.1025
2.4542
0.7842
Fund-of-Funds
161
8.8028
2.6448
3.9233
1.6305
2.423
0.6914
Total
744
16
Table 4: Comparison of top 50% Sharpe ratio funds and their 24-month rolling window clones (cont.) Rolling Window Linear Clones using the Top 50% Sharpe Ratios Convertible Arbitrage
26
3.3882
2.762
3.4932
1.935
0.9626
0.344
Dedicated Short Bias
6
0.5853
5.8714
15.9927
6.1591
-0.0045
0.4345
Emerging Markets
33
9.6637
11.7724
10.9442
8.9804
0.9067
0.4344
Equity Market Neutral
38
4.4249
3.7185
4.8375
3.1351
0.9091
0.344
Event Driven
29
5.6015
3.4671
6.0055
3.8815
0.9988
0.3946
Fixed Income Arbitrage
21
3.1678
2.5124
3.6848
2.8653
0.9242
0.39
Global Macro
31
10.9176
13.0015
11.8448
7.4104
0.8985
0.6637
Long/Short Equity Hedge
249
9.3169
5.9381
10.2498
5.3449
0.9456
0.406
Managed Futures
105
14.6192
10.4409
14.0522
8.1268
1.0538
0.5311
Multi-Strategy
45
4.6342
3.04
4.4381
2.1096
1.0525
0.407
Fund-of-Funds
161
4.2239
2.0846
3.9111
1.8051
1.0856
0.1953
Total
744
Once again, and as expected, the clones in Tables 3 and 4 offer on average more attractive Sharpe ratios. Therefore, investors seeking a more balanced risk-to-reward ratio can benefit by using replicators that target funds with historically higher Sharpe ratios, rather than replicators that use a broad hedge fund replicator approach. Even though less data is utilized, acceptable replication performance is still achieved.
4.2 The Top Return Funds and Their Clones
We now use an approach similar to selecting the desired Sharpe ratio data, but instead select the funds with highest average returns, resulting in clones with significantly higher average return. By comparing the clones in Table 5 with Table 1, we note that as expected this selection strategy improves the performance of the clones in terms of average expected returns across all fund categories, even with less data available for
17
cloning. In several cases the average Sharpe ratio has also improved, such as for Emerging Markets (0.73 with clones of selected funds vs. 0.67 with clones of all funds), Equity Market Neutral (1.27 with clones of selected funds vs. 1.12 with clones of all funds), Fixed Income Arbitrage (1.27 with clones of selected funds vs. 1.17 with clones of all funds), Long/Short Equity Hedge (0.72 with clones of selected funds vs. 0.65 with clones of all funds) and Multi-Strategy (1.07 with clones of selected funds vs. 0.93 with clones of all funds).
Table 5: Comparison of top 50% average return funds and their fixed-weight clones Sample Size
Categories
Annual Mean Return % Mean
Annual SD % SD
Mean
Annual Sharpe
SD
Mean
SD
Fixed Weight Funds using the Top 50% Average Returns Convertible Arbitrage
26
11.316
3.3154
7.9147
6.1984
2.7959
3.8328
Dedicated Short Bias
6
9.5046
3.9039
24.2565
8.161
0.4121
0.1469
Emerging Markets
33
22.5537
7.2929
22.9372
14.2013
1.4321
1.1232
Equity Market Neutral
38
10.5336
4.1885
10.3951
11.7694
1.6893
1.1723
Event Driven
29
14.9168
4.3047
10.4436
4.1972
1.5664
0.5115
Fixed Income Arbitrage
21
10.6681
2.2654
7.0426
4.7503
2.6522
3.018
Global Macro
31
18.2429
6.2664
18.5651
8.6461
1.1209
0.4683
Long/Short Equity Hedge
249
16.9964
6.2562
17.3597
8.771
1.1045
0.3926
Managed Futures
105
19.1808
6.7839
24.2593
10.9732
0.8921
0.3908
Multi-Strategy
45
13.5113
4.515
10.9939
8.8505
1.5867
0.7102
Fund-of-Funds
161
11.2613
2.6908
9.0994
5.1865
1.5212
0.6827
Total
744 Fixed Weight Linear Clones of the Top 50% Average Returns
Convertible Arbitrage
26
4.7041
4.3721
7.9147
6.1984
0.9639
0.5678
Dedicated Short Bias
6
13.3449
11.6547
24.2565
8.161
0.5965
0.4579
Emerging Markets
33
12.2406
4.7772
22.9372
14.2013
0.7332
0.4134
Equity Market Neutral
38
12.0896
13.4643
10.3951
11.7694
1.2727
0.3617
Event Driven
29
7.775
3.4856
10.4436
4.1972
0.8272
0.3905
Fixed Income Arbitrage
21
7.7895
3.9955
7.0426
4.7503
1.2716
0.4117
Global Macro
31
15.7173
12.5214
18.5651
8.6461
0.9122
0.4919
18
Table 5: Comparison of top 50% average return funds and their fixed-weight clones (cont.) Long/Short Equity Hedge
249
10.8293
7.8843
17.3597
8.771
0.7167
0.4316
Managed Futures
105
27.0129
13.84
24.2593
10.9732
1.1715
0.4175
Multi-Strategy
45
9.3475
10.145
10.9939
8.8505
1.065
0.5004
Fund-of-Funds
161
8.0408
3.8367
9.0994
5.1865
1.0628
0.4669
Total
744
Table 6 shows the results of the same selection technique now applied to a rolling window regression. A comparison of Table 6 with Table 2 shows the average return selection strategy to be effective in working with a monthly rebalancing approach that on average provides a higher expected return as compared to applying the rolling window cloning process to all funds.
With higher average returns across all fund categories, replication using the top return selection technique can be appealing to those investors targeting higher returns as compared to lower risk or higher risk-return ratios. Nonetheless, investors must be aware that this could also lead to investors taking on more risk as seen from the standard deviation of mean returns. However, the increased risk is justified across several fund categories as seen from their higher returns and improved Sharpe ratios.
Table 6: Comparison of top 50% average return funds and their 24-month rolling window clones Sample Size
Categories
Annual Mean Return % Mean
Annual SD % SD
Mean
Annual Sharpe SD
Mean
SD
Rolling Window Funds using the Top 50% Average Returns Convertible Arbitrage
26
10.5358
3.5836
6.2626
5.6932
3.708
5.8227
Dedicated Short Bias
6
7.6179
4.8209
20.4851
8.052
0.3991
0.2751
19
Table 6: Comparison of top 50% average return funds and their 24-month rolling window clones (cont.) Emerging Markets
33
21.0865
8.3094
17.0337
12.9414
1.8964
1.3299
Equity Market Neutral
38
8.7284
4.406
6.9569
6.149
1.8554
1.1948
Event Driven
29
13.3725
3.8987
7.7341
3.9111
1.9434
0.5713
Fixed Income Arbitrage
21
8.4148
2.1475
4.8131
3.5657
3.3849
4.4743
Global Macro
31
14.0056
5.6653
13.7819
6.705
1.1754
0.5381
Long/Short Equity Hedge
249
14.4895
6.5001
12.7189
7.215
1.3086
0.5006
Managed Futures
105
15.0039
5.779
19.5865
9.9743
0.9117
0.5033
Multi-Strategy
45
11.4261
3.4736
7.6796
5.3226
1.8729
0.8487
Fund-of-Funds
161
10.9119
2.6058
7.4986
4.1708
1.7936
0.8558
Total
744 Rolling Window Linear Clones using the Top 50% Average Returns
Convertible Arbitrage
26
3.3065
5.5263
6.8687
5.9018
0.747
0.6278
Dedicated Short Bias
6
0.5853
5.8714
15.9927
6.1591
-0.0045
0.4345
Emerging Markets
33
11.2535
11.8288
17.1017
9.8944
0.7245
0.4799
Equity Market Neutral
38
5.0366
4.9142
6.8257
3.8261
0.7938
0.5212
Event Driven
29
7.7623
5.4124
8.5555
3.7559
0.9633
0.5821
Fixed Income Arbitrage
21
3.3557
4.3105
5.7327
3.7228
0.8062
0.5304
Global Macro
31
9.9069
13.6159
15.9702
8.8125
0.6415
0.6749
Long/Short Equity Hedge
249
11.7083
9.3141
14.0064
7.4869
0.8822
0.4229
Managed Futures
105
21.5489
15.507
22.7806
11.8043
0.9977
0.5061
Multi-Strategy
45
7.111
6.2565
8.3659
6.0355
0.9515
0.4563
Fund-of-Funds
161
6.211
3.9986
6.8757
4.1992
0.9674
0.2894
Total
744
5. Conclusion
Our research has shown that the fund selection process has a significant impact of the performance of the clones. By setting a higher benchmark for the clones during replication, one can obtain better return performance, as expected, even though less data
20
is used during the replication process. Hence, it can be expected that clones based on strategies that choose funds with the highest Sharpe ratio, or funds with the highest average returns, can still provide similar replication performance even though less data is used as compared to replicating a larger and broader set of hedge funds. One potential drawback of this selection procedure is that at times it could be more difficult to match the higher benchmark during modeling. However, we believe that using factors that are more relevant to each strategy will yield better clone replications. Therefore, instead of always using the same ETFs during the replication process, no matter which strategy is being replicated, it may be possible to create better clones for each individual hedge fund strategy by choosing ETFs that provide more information content for the chosen strategy. This approach will be tested as a next step in an attempt to provide increased performance and replication, even when a smaller data set is provided or being modeled.
References
1.
William Fung and David A. Hsieh, 1999, “A primer on hedge funds,” Journal of Empirical Finance, 6, 309-331.
2.
http://online.wsj.com/news/articles/SB10001424052748704718204574615980132 871774
3.
http://www.morningstar.com/cover/videocenter.aspx?id=389803
4.
https://www.credit-suisse.com/us/hedge_strategies/en/liquid_alternative_beta.jsp
21 5.
http://news.morningstar.com/articlenet/article.aspx?id=631996
6.
Sharpe, William, 1992, “Asset Allocation: Management Style and Performance Measurement,” Journal of Portfolio Management, 18, 7-19.
7.
William Fung and David A. Hsieh, 1997, “Empirical characteristics of dynamic trading strategies: The case of hedge funds,” Review of Financial Studies, 10(2), 275-302.
8.
William Fung and David A. Hsieh, 2001, “The risk in hedge fund strategies: Theory and evidence from trend followers,” Review of Financial Studies, 14(2), 313-341.
9.
Jasmina Hasanhodzic and Andrew Lo, 2007, “Can hedge-fund returns be replicated?: The linear case,” Journal of Investment Management, 5(2), 5-45.
22
II. Hedge Fund Replication using Strategy Specific Factors By Sujit Subhash And David Enke
Sujit Subhash is a Graduate Research Assistant at the Department of Engineering Management and Systems Engineering, Missouri University of Science and Technology. Email:
[email protected] Dr. David Enke is a Professor and Chair of the Department of Engineering Management and Systems Engineering, Missouri University of Science and Technology. Email:
[email protected]
Abstract
Hedge funds have traditionally served wealthy individuals and institutional investors with the promise of delivering uncorrelated returns, absolute positive returns irrespective of market direction, and protecting investor capital. However, the financial crisis of 2008 has heightened investor sensitivity to the high fees, illiquidity, and lockup periods typically associated with hedge funds. The lack of transparency and extreme variation in
23
the performance of hedge funds make the due diligence process critical in selecting the right fund. In the crowded world of hedge funds, this can be expensive and time consuming. Hedge fund replication products, or clones, seek to answer these challenges faced by hedge fund investors by providing daily liquidity, complete transparency, and immediate exposure to a desired hedge fund strategy. Recent research has established that a significant part of hedge fund returns can be replicated by portfolios constructed using liquid tradable instruments. This paper examines the importance of constructing clones with factors selected based on the economic relevance to each hedge fund strategy, and then compares the clone performance against both the hedge funds and the clones constructed using a more general set of risk exposures. These clones are further compared against the top performing hedge funds to analyze if the clones continue to deliver against a higher benchmark with regard to both risk and return. Keywords: Hedge Funds, Hedge Fund Replication, Regression, Hedge Fund Strategies
24
1. Introduction
Hedge fund replication products have received a lot of attention of late as an alternative to investing in hedge funds. Hedge funds have been pessimistic to regulation and disclosure as they fear that regulation can constraint their money making abilities and that full disclosure would lead to others copying their trades. Investors were happy with the elusive and non-transparent structure of hedge funds when they delivered double digit returns and low market correlation, however, the recent economic crisis has shown that hedge funds are not entirely immune to market events (Sourd 2009).
Hedge funds engage in techniques such as shorting to protect against adverse market returns and to maintain a lower correlation to the overall market. However, studies have shown that although they exhibit low correlation and superior returns during market uptrends, they tend to be severely affected during market downturns (Agarwal and Naik 2004). Investors are beginning to question the value they receive in exchange for paying the high fees charged by hedge funds, which have typically charged a management fee of around 1-2% of assets and an incentive-based performance fee of 15-20% (Fung and Hsieh 1999). They also have not traditionally gauged their performances against a benchmark, but increased investments from institutional investors seeking more accountability, and the lack of transparency has led these institutional investors to search for alternatives in the form of hedge fund replication products that offer complete transparency, along with daily liquidity that help avoid lock-up periods associated with hedge funds. Agarwal and Naik (2000) found that performance persistence decreases as
25
the return measurement period increases, and that persistence in losers is higher than among winners, making hedge fund selection important. Malkiel and Saha (2005) also showed a lack of persistence in the performance of hedge funds.
There is also evidence that the allure of hedge funds might be overstated. Hedge fund indexes showing stellar performance include funds that are closed to new investments, with the performance of investable funds having been found to be significantly inferior to the performance of the non-investable indexes (Feldman, et al. 2009). Choosing a hedge fund that is available to new investors in another challenge that needs extensive and expensive due diligence. This is somewhat addressed by investing in fund-of-funds hedge funds, which handle the due diligence and diversification process effectively, but this comes at the cost of an additional layer of fees. Research found that the average fund-offunds hedge fund does not offer statistically significant alpha (Fung, et al. 2008), with any alpha delivered often consumed by fees (Fung and Hsieh 2007). A lack of consistency among hedge fund index providers also casts doubts over their usefulness; the heterogeneity across providers makes performance measurement of hedge fund categories difficult to analyze, and research has found convertible arbitrage to be the only truly homogenous category of hedge funds across hedge fund index providers (Kugler, et al. 2010). The effects of missing returns in hedge fund databases are often debated. However, Daniel, et al. (2012) showed that this isn’t a serious concern as missing returns of liquidated funds are offset by successful funds that choose to stop reporting. After Sharpe (1992) used an asset class factor model to decompose the performance of mutual funds, the focus shifted to hedge funds and substantial research has established
26
that a significant component of hedge fund returns are made up of systemic exposures that can be expressed in terms of liquid tradable instruments. Fung and Hsieh (2004) used a seven factor model that showed that up to 80% of the variance of returns of some broad hedge fund indexes can be explained by using a combination of equity and options based factors. Fung and Hsieh (2001) used look-back stradlles to replicate the returns of trend followers. Jaeger and Wagner (2005) used a multi-linear asset factor model that showed good results for strategies such as long/short and short bias, but performed poorly for complex strategies such as managed futures and equity market neutral. Li, et al. (2013) used factor models to highlight potential applications in hedging market exposure, for estimating daily VaR, and for forecasting the daily performance of hedge funds.
Within the last few years, researchers have also been replicating hedge fund returns (Hasanhodzic and Lo 2007; Kat and Palaro 2005), with hedge fund replication products, or clones, being a viable alternative to hedge funds for investors who are unable to meet the accreditation requirements needed to invest in hedge funds, and also to those investors challenged by the high minimum investments that hedge funds typically require. Institutional and sophisticated investors should consider hedge fund clones as they provide a significant cost advantage over hedge funds, offer daily liquidity, and are scalable to the capacity of investments that institutional investors can make. The clones also have an advantage in terms of complete transparency and ease of monitoring. The difficulty associated with selecting a hedge fund make clones an accessible choice that an investor can use to gain immediate exposure to the desired hedge fund strategy.
27
The replication attempts can be broadly classified into three categories: factor modeling, distribution replication, and rules-based replication. Distribution replication focuses the replication on the statistical properties of the hedge fund returns rather than tracking the monthly returns of the funds (Kat and Palaro 2005). This strategy is complex and can be difficult to implement, sometimes becoming more complicated than the underlying hedge fund trading strategies. Rules-based replication uses a set of defined trading rules to capture the core processes of specific hedge fund styles; a sub-category of this type of replication often used is mechanical replication. Mechanical replication seeks to mimic the holding of hedge funds, however, limitations in disclosures by hedge funds make this an ineffective strategy that suffers from lag even when copying the holdings revealed in the 13F filing of top managers. Factor based modeling offers a simple and easy to implement model that can be used to effectively replicate or clone various sub-styles of hedge funds. Hasanhodzic and Lo (2007) showed that by using a simple factor model made up of easily tradable factors, replications of funds can be achieved to a great extent.
This paper extends the analysis to cover individual hedge fund strategies by focusing on the importance of selecting the factor exposures that are economically relevant to each fund strategy. The performance of the replication models that obtain superior performance is also validated against a selection of top returning and top risk-adjusted returning funds.
2. Methodology
28
2.1. Initial motivation
Hasanhodzic and Lo (2007) showed that it is possible to construct clone portfolios that offer comparable performance to a number of hedge fund categories by using a basket of common and diverse risk factors that are easily tradable through liquid financial instruments. The hedge fund clones were constructed by regressing the individual hedge fund returns against five factors: 1) U.S. Dollar Index Return; 2) S&P 500 Total Return; 3) Spread between the Lehman Corporate Bond Index and the Lehman Treasury Index; 4) Lehman Corporate AA Intermediate Bond Index; and 5) Goldman Sachs Commodity Index Total Return. Each clone is a portfolio of the factors and these factors are used to run a constrained regression on hedge funds in each fund category to obtain portfolio weights of the risk factors in the clones. Two models are presented in the form of a fixed weight model (where the portfolio weights of the factors remain constant) and a rolling window model (where portfolio weights are rebalanced monthly). Hasanhodzic and Lo (2007) found that while the fixed weight clones performed well for a number of hedge fund strategies, the performance of the rolling window model was not quite as good. The fixed weight and rolling window models are outlined below. Fixed weight model The fixed weight model is constructed using an ordinary least squares algorithm with the regression coefficients constrained to sum to one. Dropping the intercept forces the least square algorithm to use the factors to fit the means returns of the fund, thereby giving an
29
optimized portfolio where the beta coefficients are interpreted as the factor weights in the clone for each respective fund. 𝑅𝑖𝑡 = 𝛽𝑖1𝐹1𝑡 + 𝛽𝑖2𝐹2𝑡 +…+𝛽𝑖𝑛𝐹𝑛𝑡+𝜀𝑖𝑡,
(1)
𝑡 = 1, 2…𝑇 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝛽𝑖1 + … + 𝛽𝑖𝑛 = 1 The estimated regression coefficients are used as the portfolio weights to give the portfolio returns {R*it}. {R*it} is then renormalized to obtain the clone portfolio return, {Ritclone}. 𝑅∗𝑖𝑡 = 𝛽∗𝑖1𝐹1𝑡 + 𝛽∗𝑖2𝐹2𝑡 + … +𝛽∗𝑖𝑛𝐹𝑛𝑡 𝑅𝑖𝑡𝑐𝑙𝑜𝑛𝑒 = 𝛾𝑖 𝑅∗𝑖𝑡,
𝛾𝑖 = 𝜎𝑅/ 𝜎𝑅∗
(2) (3)
The portfolio weights and renormalization factors of the fixed-weight clones stay constant over time for each clone. Rolling window model The rolling window model uses a 24-month rolling window regression to estimate the portfolio weights of the risk factors. This is a more dynamic model compared to the fixed weight model and can be seen as suitable for investors who want to actively rebalance their portfolios to capture the non-stationary nature in the hedge fund return series (Hasanhodzic and Lo 2007). Rit−k = βit1F1t−k + βit2F2t−k + …. + βitnFnt−k + εit−k k = 1, 2…24
(4)
30
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝛽𝑖𝑡1+…. +𝛽𝑖𝑡n = 1 Rebalancing is now done each month for every clone. 𝑅∗𝑖𝑡 = 𝛽∗𝑖𝑡1𝐹1𝑡 + 𝛽∗𝑖𝑡2𝐹2𝑡 + … +𝛽∗𝑖𝑡𝑛𝐹𝑛𝑡
Ritclone
=
γit R∗it,
γit =
2 √∑24 𝑘=1(𝑅𝑖𝑡−𝑘 −𝜇𝑅𝑖𝑡 ) ∗ 2 √∑24 𝑘=1(𝑅𝑖𝑡−𝑘 −𝜇𝑅∗𝑖𝑡 )
(5)
(6)
2.2. Modeling approach
Fixed-weight and rolling-window models similar to the ones used by Hasanhodzic and Lo (2007) are used to analyze a sample of 1495 hedge funds with monthly returns from August 1996 to September 2008. The rolling window model requires the calibration of the 24-month rolling window regression and renormalization factor, and hence has the first 47 months excluded from the performance comparison of the funds and clones. However, all 145 months are used for analyzing the fixed-weight model. The sample includes funds belonging to various categories, such as convertible arbitrage, dedicated short bias, emerging markets, equity market neutral, event driven, fixed income arbitrage, long/short equity, global macro, managed futures, multi-strategy, and fund-of-funds. For each strategy, the factors used in the model are selected based on the characteristics of the underlying hedge fund category. The performance of the clones developed using these factors are compared to the funds and the clones constructed from the factors listed in section 2.
31
Three data selection procedures are used in the construction of the hedge fund clones that will give investors a more customizable clone model that offers the choice between the clones constructed using all funds, funds with higher Sharpe ratios, and funds with higher average returns. The performance of the clones constructed from factors specific to each hedge fund are again compared against those of the top performing funds to analyze if these clones continue to deliver better performance against a higher benchmark. Throughout the remainder of the paper, clone2 stands for the clones constructed from the factors considered specifically for each individual hedge fund category, while clone1 represents the clones that used the general set of factors listed in section 2, and previously used by Hasanhodzic and Lo (2007).
3. Strategy Overview
This section provides an overview of each hedge fund strategy and lists the factors used to construct clone2 under each category. The factors used to model clone2 are selected specifically for each hedge fund strategy. 3.1. Convertible Arbitrage
The convertible arbitrage category of hedge funds is a relative value strategy focused on capturing inefficiencies in the convertible bond market. Around $40 billion was under management in convertible arbitrage funds as of 2010, returning an average of 9.3%
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annualized with a volatility of 7.7% between 1994 and 2010 (Credit Suisse 2011). A strategy utilized by these funds involves going long a convertible bond and taking a short position in the underlying stock. The hedge can also be in the form of credit default swaps, as well as interest rate and volatility derivatives. However, hedging only equity risk is more characteristic of convertible arbitrage hedge funds (Agarwal, et al. 2011).
The convertible bond market is very illiquid and the majority of the positions are held by convertible arbitrage funds. Although this illiquidity is often the source of their returns, it can quickly squeeze the funds into liquidating the bonds at losses during a credit crunch. The factors used to form the clones are selected with the goal of maintaining an overall consistency with the investment objectives of the respective hedge funds. The factors selected to form the convertible arbitrage clone include the following: 1) Large Cap US Stocks: S&P 500 Total Return. 2) Bond: Lehman Corporate AA Intermediate Bond Index. 3) High Yield Bond: Merrill Lynch High Yield Master 2 Index.
3.2. Dedicated Short Bias
Dedicated short bias funds take both long and short exposures to equities while maintaining a net short position. This category performs well when the markets are in a
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down-trend, but suffers in bull markets. Managers change their net short exposure according to their outlook on the overall market. The factors used to replicate this strategy include the following: 1) Large Cap US Stocks: S&P 500 Total Return. 2) Small Cap US Stocks: Russell 2000 Small-Cap Index. 3) Treasury Rates: Lehman Treasury Index.
3.3. Emerging Market
Emerging market hedge funds seek to exploit opportunities developed by political, currency, credit, and interest rate uncertainties that occur in emerging markets, while also investing in their corresponding equity markets. These opportunities are also used by global macro and event driven hedge funds. The factors used to develop emerging market clones include the following: 1) Emerging Market: MSCI Emerging Market Index. 2) High Yield Bond: Merrill Lynch High Yield Master 2 Index. 3) Bond: Lehman Corporate AA Intermediate Bond Index. 4) Currency: U.S. Dollar Index Return.
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5) Credit Spreads: The spread between the Lehman Corporate Bond Index and the Lehman Treasury Index.
3.4. Equity Market Neutral
Equity Market Neutral (EMN) hedge funds aim to exploit certain opportunities presented by a specific group of stocks while staying neutral to the broad market. This strategy sometimes overlaps with relative value and long/short equity. It performed relatively well, losing fewer than 3% on average in 2008 and had the lowest volatility in a ten-year window between July 1999 and June 2009 (Low 2009). Equity market neutral managers perform frequent to moderate rebalancing of their portfolio to maintain market neutrality.
Although they are broadly market-neutral, EMN funds have exposures to a wide range of equity classes. Value and momentum factors perform well in different market environments and hence offer a balance to the portfolio. EMN funds also have exposures to the US and emerging market equities, and high yield bonds (Feldman, et al. 2009). The factors used to construct the EMN clone include the following: 1) Market Momentum: MSCI USA Momentum Index. 2) Large Cap US Stocks: S&P 500 Total Return. 3) Value Stocks: MSCI USA Value Index.
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4) Emerging Market: MSCI Emerging Market Index. 5) High Yield Bond: Merrill Lynch High Yield Master 2 Index. 6) Bond: Lehman Corporate AA Intermediate Bond Index.
3.5. Event Driven
The event driven category of hedge funds capitalizes on opportunities that develop in the short-term, causing mispricing in equities, bonds, and global markets. Key events can include mergers, acquisitions, and corporate restructuring. Event driven hedge funds perform poorly during down trending markets as deals are more likely to fall through during those times (Agarwal and Naik 2004). The factors used to replicate the event driven strategy include: 1) High Yield Bond: Merrill Lynch High Yield Master 2 Index. 2) Emerging Market: MSCI Emerging Market Index. 3) Value Stocks: MSCI USA Value Index. 4) Small Cap US Stocks: Russell 2000 Small-Cap Index.
3.6. Fixed Income Arbitrage
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Fixed Income arbitrage is another relative value strategy used to exploit bond market inefficiencies. As of 2010, these funds have about $120 billion worth of assets under management and have delivered an average of 5.3% annualized return with 6% volatility between 1994 and 2010 (Credit Suisse 2011). This strategy performs well in a low volatility environment. However, it is particularly susceptible to crowed trades and needs to take on very high leverage to deliver substantial returns. The strategy typically profits by holding long positions in higher yielding bonds and short positions in lower yielding bonds. This strategy is known to have exposure to fixed income spreads, and though a number of spread combinations can be chosen as a factor, the credit spread is the best option because of its’ long history and how widening credit spreads usually result in other spreads also widening (Fung and Hsieh 2002) .
The Long-Term Capital Management story stands out to underscoring the risks prevalent with fixed income arbitrage trades as crowding out the yield spread trade can cause the spreads to narrow, thereby limiting the possible return, causing the funds to take on more risk with higher leverage and potential margin calls (Jorion 2000). The factors selected to form the fixed income arbitrage clone include the following: 1) Credit Spreads: the spread between the Lehman Corporate Bond Index and the Lehman Treasury Index. 2) Large Cap US Stocks: S&P 500 Total Return. 3) Bond: Lehman Corporate AA Intermediate Bond Index.
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4) High Yield Bond: Merrill Lynch High Yield Master 2 Index.
3.7. Global Macro
The global macro hedge fund is a category that especially appeals to institutional investors due to its liquidity. Global macro is one of the few hedge fund strategies that lost fewer than 5% in 2008 when most hedge fund strategies had double-digit percentage losses (Low 2009). Its robustness can be seen in its performance between 2000 and 2010 where it returned an average of near 12% annualized return with a volatility of 5.5%, illustrating how the strategies of global macro funds perform well in volatile market environments, with about $290 billion under management (Casano 2010). The global macro strategy invests in a very broad range of asset classes and geographies.
The factors used to construct the clones of global macro include the following: 1) Bond: Lehman Corporate AA Intermediate Bond Index. 2) Large Cap US Stocks: S&P 500 Total Return. 3) Emerging Market: MSCI Emerging Market Index. 4) Currency: U.S. Dollar Index Return. 5) Commodity: Goldman Sachs Commodity Index Total Return.
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3.8. Long/Short Equity
Long/Short hedge funds take both long and short positions in a broad range of equity classes spread across different size, style, and regions. These funds benefit from a positive equity environment and delivered an annualized return of 9.5% with 10.6% volatility between January 1998 and October 2009. This strategy will underperform longonly strategies during a strong bull market, however, the long-short strategy will outperform over a full market cycle (Bruce and Reynolds 2010) .
The long/short strategy has become the most established hedge fund strategy with over 30% of all the assets under management in hedge funds invested in long/short funds, comprising over 43% of all hedge funds (Feldman, et al. 2009). Although these funds are typically long biased, their strategies sometimes overlap those of equity market neutral funds in times of market downturns. The factors used to construct the clones for long/short equity hedge funds include a wide range of equity factors to which the funds usually have exposures. The factors used to construct long/short clones include the following: 1) Large Cap US Stocks: S&P 500 Total Return. 2) Small Cap US Stocks: Russell 2000 Small Cap Index. 3) Developed International Markets: MSCI EAFE Index. 4) Market Momentum: MSCI USA Momentum Index.
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5) Bond: Lehman Corporate AA Intermediate Bond Index.
3.9. Managed Futures
Managed futures hedge funds seek to capture returns by capitalizing on trends across a range of asset classes, including equities, commodities, fixed income, and currencies. Managed futures was the best performing hedge fund strategy in 2008, returning over 16% when most of the other strategies ended the year in negative territory and had over $330 billion in assets under management by the end of 2012 (Drachman 2013). The strategy also has a very low correlation to broad market indices and has returned over 8.6% annualized with 12.2% volatility between September 2000 and September 2010 (Casano 2010).
The flexibility of this strategy also results in high variation in the performance between different managers. The best performing managed futures fund in 2012 returned over 13%, while the worst performer lost over 27%, yet these funds have the ability to capture both uptrends and down trends and have a history performing well in either trend markets (Till and Eagleeye 2011). The managed futures strategy returned over 35% during the tech downturn between September 2000 and December 2002 and over 31% in the following market bull run ending in October 2007 (Drachman 2013). The factors used to replicate the managed futures funds include the following:
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1) Currency: U.S. Dollar Index Return. 2) Treasury Rates: Lehman Treasury Index. 3) Commodity: Goldman Sachs Commodity Index Total Return. 4) Large Cap US Stocks: S&P 500 Total Return. 5) Market Volatility: CBOE Volatility Index.
3.10. Multi-Strategy
Multi-Strategy hedge funds often develop from successful single strategy funds that extend their services to accommodate incoming capital when it reaches a capacity that managers see as the optimum threshold beyond which they believe that they will be inefficient in using fresh capital towards a single strategy. This category can be expected to offer diversification, higher capacity, and consistency in the long term. The factors used to construct multi-strategy clones include the following: 1) Credit Spreads: The spread between the Lehman Corporate Bond Index and the Lehman Treasury Index. 2) Large Cap US Stocks: S&P 500 Total Return. 3) High Yield Bond: Merrill Lynch High Yield Master 2 Index. 4) Emerging Market: MSCI Emerging Market Index.
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5) Bond: Lehman Corporate AA Intermediate Bond Index.
3.11. Fund-of-Funds
This fund-of-funds hedge fund category is used by investors who want to construct a portfolio of hedge funds in order to increase diversification and decrease correlation to the overall markets. Constructing a portfolio of hedge funds requires extensive due diligence and access to performance information that is not easily available. Fund-offunds hedge funds take care of the due diligence, manager selection, and risk monitoring in exchange for an additional layer of fees, typically in the range of 10% asset management fees and 1% performance fees. Fund-of-funds hedge funds can vary from one another in terms of the weighting to different managers, liquidity, strategy exposures, and extent of rebalancing between the managers (Suppal and Garza 2012). The factors selected to clone the fund-of-funds include the following: 1) Credit Spreads: The spread between the Lehman Corporate Bond Index and the Lehman Treasury Index. 2) Large Cap US Stocks: S&P 500 Total Return. 3) High Yield Bond: Merrill Lynch High Yield Master 2 Index. 4) Emerging Market: MSCI Emerging Market Index. 5) Bond: Lehman Corporate AA Intermediate Bond Index.
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4. Results
This section discusses the results of the replication process using the fixed weight and rolling window clone models discussed in section 2, and then compares the benefits of selecting factors specific to the underlying hedge fund strategy versus simply using a broad set of factors covering basic sources of risk associated with stocks, bonds, currency, credit, and commodities. While the fixed weight model is suitable for investors wanting a more passive approach to using their hedge fund clones, the rolling window model is more for investors that prefer active monthly rebalancing. Also covered in this section are the results of the clones constructed from the funds with the highest Sharpe ratios and the funds with the best average returns. The selection bias inherent in the cloning process is used to the benefit of the investors to allow for more customization of the clones and the ability to model them according to their preferences for risk and return. Investors prioritizing a more balanced risk-reward ratio can choose the clones constructed from the top Sharpe ratio funds, while investors seeking higher raw returns can use the clones constructed from the top returning funds.
4.1. All Funds
Table 1 shows the performance comparison for the clones created using all funds for the fixed weight model. The results for clone2 are impressive across several categories and
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are significantly better than that of clone1 for all hedge fund strategies, with the exception of dedicated short bias and managed futures. Please note that one of the goals in selecting factors specific to the hedge fund strategy is to obtain clones with mean returns closer to that of the hedge funds. Therefore, in the case of managed futures, although clone1 has higher average mean return (22.12% clone1 vs. 15.37% clone2 vs. 13.57% funds), the performance of clone2 is preferable given that both its return is closer to the actual funds, and the standard deviation among mean returns is lower than clone1. In the case of dedicated short bias, although clone1 appears to have an average mean return closer to that of the fund, the higher standard deviation among mean returns, combined with the lower Sharpe ratio, makes clone2 the preferred choice. Equity market neutral provides for an interesting observation with clone2 providing much higher mean returns, but with comparable variance in mean returns. They also have very close Sharpe ratios (1.43 clone2 vs. 1.45 clone1).
The average mean return of clone2 is strikingly close to the average mean return of the funds in the case of convertible arbitrage (8.17% clone2 vs. 8.64% funds), emerging markets (17.04% clone2 vs. 16.80 funds), fixed income arbitrage (7.88% clone2 vs. 8.52% funds), long/short equity hedge (11.73% clone2 vs. 12.35% funds), and fund-offunds (9.46% clone2 vs. 9.13% funds). The standard deviation among mean returns is also close in these cases. Multi-Strategy also offers clones with comparable mean returns and Sharpe ratio. The average Sharpe ratio of clone2 is higher than that of clone1 in all cases except managed futures, and is close to the mean Sharpe ratio of the funds for several categories. As illustrated by the results in Table 1, clone2 is the preferred over
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clone1 for all hedge fund strategies when constructed using all funds, and provides notably close performance to the funds in most cases.
The rolling window comparison of the performance of both the clones and that of the corresponding funds for all the funds is provided in Table 2. These results show that clone2 remains the preferred choice among all hedge fund strategies.
Clone2 continues to offer highly comparable performance to the funds with the rolling window model having a few exceptions coming in the categories of event driven, fixed income arbitrage, and multi-strategy. Convertible arbitrage (10.11% clone2 vs. 8.91% funds) and global macro (14.83% clone2 vs. 13.05% funds) have higher average mean returns for the clone2 models, although the variance in mean returns is much higher for global macro clones2 (11.88% clone2 vs. 6.37% funds). However, the comparable Sharpe ratios (1.16 clone2 and 1.1 funds) make it a clone worth considering. Emerging markets and fund-of-funds categories have their clones2 perform close to the funds in terms of mean returns, while having slightly higher variance in mean returns. Long/short equity hedge and equity market neutral strategies have the clone2 models perform remarkably well, both in terms of their average mean returns and the variance in mean returns.
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Table 1: Performance comparison for fixed weight model for all funds and their clones Fixed Weight Model - All Funds Sample Annual Mean Categories Annual SD % Size Return % Mean SD Mean SD Funds Convertible Arbitrage 53 8.64 3.72 6.30 4.79 Clone1 Convertible Arbitrage 53 4.70 3.22 6.30 4.79 Clone2 Convertible Arbitrage 53 8.17 3.06 6.30 4.79 Funds Dedicated Short Bias 13 4.82 5.46 23.18 8.69 Clone1 Dedicated Short Bias 13 8.05 9.23 23.18 8.69 CLone2 Dedicated Short Bias 13 11.82 6.33 23.18 8.69 Funds Emerging Markets 67 16.80 7.99 18.78 11.89 Clone1 Emerging Markets 67 9.37 4.90 18.78 11.89 CLone2 Emerging Markets 67 17.04 8.14 18.78 11.89 Funds Equity Market Neutral 76 7.65 4.32 9.15 9.60 Clone1 Equity Market Neutral 76 9.44 10.41 9.15 9.60 CLone2 Equity Market Neutral 76 10.48 5.32 9.15 9.60 Funds Event Driven 59 10.68 5.42 8.56 4.23 Clone1 Event Driven 59 6.40 3.08 8.56 4.23 CLone2 Event Driven 59 7.79 4.69 8.56 4.23 Funds Fixed Income Arbitrage 42 8.52 2.79 6.69 4.13 Clone1 Fixed Income Arbitrage 42 6.62 3.48 6.69 4.13 CLone2 Fixed Income Arbitrage 42 7.88 4.14 6.69 4.13 Funds Global Macro 62 13.39 6.82 15.00 7.78 Clone1 Global Macro 62 13.86 10.15 15.00 7.78 CLone2 Global Macro 62 16.88 8.02 15.00 7.78 Funds Long/Short Equity Hedge 498 12.35 6.69 14.41 7.95 Clone1 Long/Short Equity Hedge 498 8.15 6.80 14.41 7.95 CLone2 Long/Short Equity Hedge 498 11.73 5.20 14.41 7.95 Funds Managed Futures 211 13.57 7.60 18.85 10.26 Clone1 Managed Futures 211 22.12 12.45 18.85 10.26 CLone2 Managed Futures 211 15.37 8.98 18.85 10.26 Funds Multi Strategy 91 9.35 5.75 9.42 7.34 Clone1 Multi Strategy 91 6.81 7.92 9.42 7.34 CLone2 Multi Strategy 91 10.42 8.99 9.42 7.34 Funds Fund of Funds 323 9.13 3.00 7.65 4.84 Clone1 Fund of Funds 323 6.76 3.29 7.65 4.84 CLone2 Fund of Funds 323 9.46 4.26 7.65 4.84
Annual Sharpe Mean 2.33 1.03 1.55 0.18 0.37 0.57 1.23 0.67 1.09 1.45 1.12 1.43 1.44 0.84 0.90 2.14 1.17 1.31 0.99 1.00 1.24 0.97 0.65 0.94 0.79 1.24 0.84 1.35 0.93 1.25 1.47 1.05 1.37
SD 3.24 0.46 0.38 0.26 0.37 0.28 0.99 0.42 0.43 1.40 0.39 0.39 0.76 0.36 0.21 2.55 0.45 0.36 0.46 0.48 0.43 0.44 0.41 0.38 0.38 0.40 0.26 0.85 0.53 0.55 0.65 0.41 0.33
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Table 2: Performance comparison for rolling window model for all funds and their clones Categories
Funds Convertible Arbitrage Clone1 Convertible Arbitrage Clone2 Convertible Arbitrage Funds Dedicated Short Bias Clone1 Dedicated Short Bias CLone2 Dedicated Short Bias Funds Emerging Markets Clone1 Emerging Markets CLone2 Emerging Markets Funds Equity Market Neutral Clone1 Equity Market Neutral CLone2 Equity Market Neutral Funds Event Driven Clone1 Event Driven CLone2 Event Driven Funds Fixed Income Arbitrage Clone1 Fixed Income Arbitrage CLone2 Fixed Income Arbitrage Funds Global Macro Clone1 Global Macro CLone2 Global Macro Funds Long/Short Equity Hedge Clone1 Long/Short Equity Hedge CLone2 Long/Short Equity Hedge Funds Managed Futures Clone1 Managed Futures CLone2 Managed Futures Funds Multi Strategy Clone1 Multi Strategy CLone2 Multi Strategy Funds Fund of Funds Clone1 Fund of Funds CLone2 Fund of Funds
Rolling Window Model - All Funds Sample Annual Mean Annual SD % Size Return % Mean SD Mean SD 53 8.91 4.62 5.54 4.56 53 2.45 4.24 5.66 4.54 53 10.11 4.95 6.17 4.51 13 3.37 4.84 18.98 8.31 13 -1.05 5.99 15.93 6.41 13 7.58 3.57 14.92 5.77 67 21.50 10.60 15.43 9.80 67 9.53 9.20 14.64 8.81 67 19.69 13.36 14.56 8.97 76 7.16 5.20 7.66 7.14 76 4.15 5.24 7.20 6.53 76 7.69 5.55 7.41 7.30 59 11.48 5.72 7.11 3.41 59 5.86 4.58 7.75 4.30 59 7.63 5.80 7.59 4.48 42 8.83 3.13 4.64 2.72 42 3.04 3.49 5.03 3.45 42 4.14 2.54 4.97 3.54 62 13.05 6.37 13.38 6.18 62 9.05 10.92 13.55 7.54 62 14.83 11.88 13.34 7.32 498 12.90 7.63 12.24 6.74 498 9.94 8.40 12.47 6.75 498 11.21 6.72 11.92 6.71 211 12.21 7.08 17.43 9.75 211 16.01 13.39 17.78 10.74 211 14.38 12.72 17.23 10.68 91 9.96 5.36 7.45 5.40 91 4.02 8.51 8.32 6.33 91 6.61 10.63 8.31 6.23 323 9.32 3.49 6.20 4.25 323 5.16 3.39 5.83 4.19 323 8.38 6.47 5.82 4.11
Annual Sharpe Mean 3.02 0.59 1.88 0.17 -0.16 0.58 1.77 0.73 1.40 1.75 0.65 1.18 1.81 0.86 1.10 3.13 0.79 1.03 1.10 0.69 1.16 1.19 0.83 1.05 0.81 0.92 0.87 1.75 0.77 1.06 1.88 0.96 1.45
SD 5.09 0.58 0.47 0.39 0.47 0.30 1.15 0.40 0.35 2.46 0.55 0.47 0.90 0.52 0.46 4.25 0.49 0.46 0.54 0.65 0.64 0.54 0.47 0.48 0.49 0.49 0.51 1.11 0.67 0.79 0.84 0.29 0.29
The results for rolling window and fixed weight clone2 models for all funds show that selecting the factors relevant to the underlying hedge fund strategy will offer significant benefits, both in terms of replication quality and overall performance of the clones. Next
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we analyze the results of the clones using these models for the top funds in terms of both risk-reward and raw returns.
4.2. Top 50% Sharpe Ratios
In this section we look at the performance of clones constructed from the top 50% of the funds having the highest Sharpe ratios. The clones generated from these funds will benefit from the balanced risk reward properties of its corresponding funds. Although matching this higher benchmark is more difficult, using the relevant factors significantly improves the performance of the clones. Clone2 continues to outperform clone1 in terms of replication quality across all hedge fund strategies.
Table 3 offers the comparison of the fixed weight clones and the funds selected under this strategy. It can be seen that despite the challenges of a higher benchmark, clones2 still offers significantly comparable performance across many categories, including emerging markets (15.81% clone2 and 17.98% funds), equity market neutral (7.68% clone2 and 8.89% funds), long/short equity (11.54% clone2 and 13.85% funds), fund-of-funds (7.52% clone2 and 9.12% funds), multi-strategy (8.38% clone2 and 10.76% funds), managed futures (13.35% clone2 and 15.11% funds) and global macro (14.98% clone2 and 15.51% funds). There is also a similar variance in mean returns for clone2 and their corresponding funds for these strategies.
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Table 3: Performance comparison for fixed weight model for top 50% Sharpe ratio funds and their clones
Funds Clone1 Clone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2
Fixed Weight Model - Top 50 % Sharpe Ratios Funds Sample Annual Mean Categories Annual SD % Size Return % Mean SD Mean SD Convertible Arbitrage 26 9.56 3.60 4.13 2.13 Convertible Arbitrage 26 4.68 2.05 4.13 2.13 Convertible Arbitrage 26 6.50 2.70 4.13 2.13 Dedicated Short Bias 6 9.50 3.90 24.26 8.16 Dedicated Short Bias 6 13.34 11.65 24.26 8.16 Dedicated Short Bias 6 13.82 8.45 24.26 8.16 Emerging Markets 33 17.98 6.99 13.09 8.57 Emerging Markets 33 10.00 4.68 13.09 8.57 Emerging Markets 33 15.81 8.00 13.09 8.57 Equity Market Neutral 38 8.89 3.75 4.92 2.41 Equity Market Neutral 38 6.00 3.30 4.92 2.41 Equity Market Neutral 38 7.68 3.49 4.92 2.41 Event Driven 29 11.48 5.59 6.51 3.58 Event Driven 29 6.09 2.63 6.51 3.58 Event Driven 29 7.78 3.26 6.51 3.58 Fixed Income Arbitrage 21 8.93 2.66 3.79 1.73 Fixed Income Arbitrage 21 5.65 3.00 3.79 1.73 Fixed Income Arbitrage 21 5.85 2.88 3.79 1.73 Global Macro 31 15.51 6.88 12.16 6.50 Global Macro 31 11.78 6.30 12.16 6.50 Global Macro 31 14.98 7.33 12.16 6.50 Long/Short Equity Hedge 249 13.85 6.85 11.13 5.70 Long/Short Equity Hedge 249 9.26 6.99 11.13 5.70 Long/Short Equity Hedge 249 11.54 4.94 11.13 5.70 Managed Futures 105 15.11 7.46 15.60 8.29 Managed Futures 105 18.66 11.35 15.60 8.29 Managed Futures 105 13.35 7.81 15.60 8.29 Multi Strategy 45 10.77 4.73 5.60 2.80 Multi Strategy 45 6.49 4.18 5.60 2.80 Multi Strategy 45 8.38 5.51 5.60 2.80 Fund of Funds 161 9.12 2.66 4.86 1.85 Fund of Funds 161 6.20 2.94 4.86 1.85 Fund of Funds 161 7.52 3.30 4.86 1.85
Annual Sharpe Mean 3.68 1.25 1.69 0.41 0.60 0.62 1.82 0.95 1.38 2.31 1.26 1.63 1.95 1.04 1.31 3.37 1.47 1.53 1.35 1.02 1.31 1.30 0.85 1.13 1.04 1.27 0.87 2.03 1.18 1.47 1.98 1.28 1.54
SD 4.24 0.31 0.26 0.15 0.46 0.33 1.12 0.41 0.37 1.54 0.32 0.28 0.73 0.34 0.30 3.17 0.28 0.20 0.37 0.37 0.37 0.35 0.36 0.31 0.37 0.43 0.24 0.58 0.31 0.28 0.50 0.26 0.20
Fixed income arbitrage, event driven, and convertible arbitrage categories have the clones underperform their corresponding funds. These strategies largely gain from illiquidity
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risk and have significant left tail exposure; the top Sharpe ratio criterion is therefore likely to select the funds with the most illiquid exposures, making them more challenging to replicate. Table 4: Performance comparison for rolling window model for top 50% Sharpe ratio funds and their clones
Funds Clone1 Clone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2
Rolling Window Model - Top 50 % Sharpe Ratios Funds Sample Annual Mean Categories Annual SD % Size Return % Mean SD Mean SD Convertible Arbitrage 26 9.71 4.08 3.67 1.93 Convertible Arbitrage 26 3.39 2.76 3.49 1.94 Convertible Arbitrage 26 8.26 5.01 3.91 2.21 Dedicated Short Bias 6 7.13 4.01 18.93 8.65 Dedicated Short Bias 6 0.59 5.87 15.99 6.16 Dedicated Short Bias 6 8.88 4.53 15.20 5.46 Emerging Markets 33 20.38 9.20 11.01 8.13 Emerging Markets 33 9.66 11.77 10.94 8.98 Emerging Markets 33 17.68 15.98 11.11 9.32 Equity Market Neutral 38 8.61 3.86 4.33 2.19 Equity Market Neutral 38 4.42 3.72 4.84 3.14 Equity Market Neutral 38 5.58 3.87 4.77 3.08 Event Driven 29 11.90 5.69 5.49 2.88 Event Driven 29 5.60 3.47 6.01 3.88 Event Driven 29 6.64 4.08 5.73 3.61 Fixed Income Arbitrage 21 8.69 2.98 2.98 1.52 Fixed Income Arbitrage 21 3.17 2.51 3.68 2.87 Fixed Income Arbitrage 21 3.62 2.37 3.50 2.63 Global Macro 31 15.26 6.16 10.89 5.54 Global Macro 31 10.92 13.00 11.84 7.41 Global Macro 31 15.79 14.46 11.53 7.11 Long/Short Equity Hedge 249 14.03 7.53 9.47 4.78 Long/Short Equity Hedge 249 9.32 5.94 10.25 5.34 Long/Short Equity Hedge 249 10.11 5.03 9.77 5.28 Managed Futures 105 13.49 6.36 14.08 7.63 Managed Futures 105 14.62 10.44 14.05 8.13 Managed Futures 105 11.67 8.75 13.59 8.21 Multi Strategy 45 10.90 4.42 4.54 2.26 Multi Strategy 45 4.63 3.04 4.44 2.11 Multi Strategy 45 6.12 4.08 4.50 2.14 Fund of Funds 161 9.10 2.47 3.94 1.67 Fund of Funds 161 4.22 2.08 3.91 1.81 Fund of Funds 161 6.08 3.46 3.90 1.82
Annual Sharpe Mean 4.85 0.96 2.08 0.45 0.00 0.68 2.40 0.91 1.59 2.87 0.91 1.22 2.37 1.00 1.22 4.75 0.92 1.18 1.51 0.90 1.35 1.54 0.95 1.15 1.09 1.05 0.92 2.62 1.05 1.32 2.50 1.09 1.52
SD 6.84 0.34 0.20 0.39 0.43 0.40 1.34 0.43 0.36 3.08 0.34 0.42 0.90 0.39 0.41 5.60 0.39 0.46 0.43 0.66 0.72 0.44 0.41 0.47 0.53 0.53 0.51 0.90 0.41 0.49 0.69 0.20 0.20
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The rolling window results of the clones and the selected hedge funds are provided in Table 4. As seen in the table, clone2 outperforms clone1 in all hedge fund categories with the exception of managed futures, where clone2 still offers comparable performance to the funds. The most notable clone performances are for convertible arbitrage (8.26% clone2 vs. 9.71% funds), dedicated short bias (8.88% clone2 vs. 7.13% funds), and global macro (15.79% clone2 vs. 15.26% funds). While the standard deviation in mean returns are also close for convertible arbitrage and dedicated short bias, the standard deviation in mean returns for global macro clone2 is significantly higher than that for the funds. The comparable Sharpe ratios indicate that clone2 offers some benefits. Clone2 for the rest of the categories perform poorly in terms of mean returns, but the benefit of choosing the factors with consideration to the hedge fund strategy is clearly evident in the significantly higher average Sharpe ratios relative to clone1 across every strategy except managed futures.
4.3. Top 50% Returns
In this section we see the performance of clones constructed from the top 50% of funds with the best average returns. These clones are for investors who prioritize seeking higher returns and benefit from this focus in constructing the clones. Clone2 again outperforms clone1 in terms of replication quality for all strategies and in terms of average returns and Sharpe ratio for all categories except managed futures, but clone2 remains the preferred
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clone model. The top 50% Sharpe ratio funds and top 50% return funds are the same for dedicated short bias category. Table 5: Performance comparison for fixed weight model for top 50% return funds and their clones
Funds Clone1 Clone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2
Fixed Weight Model - Top 50 % Return Funds Sample Annual Mean Categories Annual SD % Size Return % Mean SD Mean SD Convertible Arbitrage 26 11.32 3.32 7.91 6.20 Convertible Arbitrage 26 4.70 4.37 7.91 6.20 Convertible Arbitrage 26 8.49 3.27 7.91 6.20 Dedicated Short Bias 6 9.50 3.90 24.26 8.16 Dedicated Short Bias 6 13.34 11.65 24.26 8.16 Dedicated Short Bias 6 13.82 8.45 24.26 8.16 Emerging Markets 33 22.55 7.29 22.94 14.20 Emerging Markets 33 12.24 4.78 22.94 14.20 Emerging Markets 33 21.41 8.96 22.94 14.20 Equity Market Neutral 38 10.53 4.19 10.40 11.77 Equity Market Neutral 38 12.09 13.46 10.40 11.77 Equity Market Neutral 38 11.11 5.79 10.40 11.77 Event Driven 29 14.92 4.30 10.44 4.20 Event Driven 29 7.78 3.49 10.44 4.20 Event Driven 29 9.66 4.44 10.44 4.20 Fixed Income Arbitrage 21 10.67 2.27 7.04 4.75 Fixed Income Arbitrage 21 7.79 4.00 7.04 4.75 Fixed Income Arbitrage 21 9.04 4.89 7.04 4.75 Global Macro 31 18.24 6.27 18.57 8.65 Global Macro 31 15.72 12.52 18.57 8.65 Global Macro 31 18.85 8.80 18.57 8.65 Long/Short Equity Hedge 249 17.00 6.26 17.36 8.77 Long/Short Equity Hedge 249 10.83 7.88 17.36 8.77 Long/Short Equity Hedge 249 13.67 5.82 17.36 8.77 Managed Futures 105 19.18 6.78 24.26 10.97 Managed Futures 105 27.01 13.84 24.26 10.97 Managed Futures 105 19.91 9.49 24.26 10.97 Multi Strategy 45 13.51 4.52 10.99 8.85 Multi Strategy 45 9.35 10.15 10.99 8.85 Multi Strategy 45 14.67 9.58 10.99 8.85 Fund of Funds 161 11.26 2.69 9.10 5.19 Fund of Funds 161 8.04 3.84 9.10 5.19 Fund of Funds 161 11.31 4.56 9.10 5.19
Annual Sharpe Mean 2.80 0.96 1.39 0.41 0.60 0.62 1.43 0.73 1.14 1.69 1.27 1.39 1.57 0.83 0.93 2.65 1.27 1.39 1.12 0.91 1.13 1.10 0.72 0.88 0.89 1.17 0.86 1.59 1.07 1.44 1.52 1.06 1.38
SD 3.83 0.57 0.47 0.15 0.46 0.33 1.12 0.41 0.42 1.17 0.36 0.44 0.51 0.39 0.23 3.02 0.41 0.27 0.47 0.49 0.42 0.39 0.43 0.35 0.39 0.42 0.25 0.71 0.50 0.38 0.68 0.47 0.38
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The fixed weight model performance for the clones and funds that are selected using the higher returns strategy are provided in Table 5. Extremely good clones are obtained for emerging markets (21.41% clone2 vs. 22.55% funds) and equity market neutral (11.11% clone2 vs.10.53% funds) given their close variation in mean returns. Global macro and managed futures categories give performance very close to their respective funds for clone2 in terms of both average mean returns and Sharpe ratios. Fixed income arbitrage (9.04% clone2 vs. 10.67% funds), multi-strategy (14.67% clone2 vs. 13.51% funds), and fund-of-funds (11.31% clone2 vs. 11.26% funds) also exhibit good replication results. Long/short equity, event driven, convertible arbitrage, and dedicate short bias had poor replication performance, but the value of using the strategy specific factors can clearly be seen both in terms of average mean returns and Sharpe ratios relative to clone1.
Table 6 presents the performance results for the rolling window model for the clones and funds selected for the higher return strategy. Clone2 again provides a better replication performance relative to clone1 across all hedge fund categories and has better overall performance in terms of average returns and Sharpe ratio for all fund strategies except managed futures. As before for managed futures, clone2 is still preferred to clone1. Event driven is the worst performing clone2 in terms of difference in average mean returns (9.39% clone2 vs. 15.98% funds). This is the only category that performed poorly on all clone2 models. Fixed income arbitrage clone2 also performed poorly (4.5% clone2 vs. 10.72% funds). In general, this category also performed poorly for the other rolling window data selection strategies tested. Fung and Hsieh (2002) demonstrated that fixed income arbitrage funds have primarily static exposures and the nature of fixed income
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arbitrage funds may cause it to perform poorly when used to model rolling window clones where the portfolio weights in a clone are rebalanced each month.
Table 6: Performance comparison for rolling window model for top 50% return funds and their clones
Funds Clone1 Clone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2 Funds Clone1 CLone2
Rolling Window Model - Top 50 % Return Funds Sample Annual Mean Categories Annual SD % Size Return % Mean SD Mean SD Convertible Arbitrage 26 12.10 4.47 7.14 5.96 Convertible Arbitrage 26 3.31 5.53 6.87 5.90 Convertible Arbitrage 26 10.51 5.65 7.32 5.69 Dedicated Short Bias 6 7.13 4.01 18.93 8.65 Dedicated Short Bias 6 0.59 5.87 15.99 6.16 Dedicated Short Bias 6 8.88 4.53 15.20 5.46 Emerging Markets 33 27.85 10.74 18.73 11.68 Emerging Markets 33 11.25 11.83 17.10 9.89 Emerging Markets 33 24.31 15.91 17.16 10.25 Equity Market Neutral 38 10.13 5.32 8.26 7.37 Equity Market Neutral 38 5.04 4.91 6.83 3.83 Equity Market Neutral 38 7.29 5.11 6.91 3.99 Event Driven 29 15.98 4.59 8.65 3.18 Event Driven 29 7.76 5.41 8.56 3.76 Event Driven 29 9.39 4.08 8.53 3.83 Fixed Income Arbitrage 21 10.72 3.07 5.33 3.36 Fixed Income Arbitrage 21 3.36 4.31 5.73 3.72 Fixed Income Arbitrage 21 4.51 2.29 5.63 3.96 Global Macro 31 17.05 6.36 16.15 6.45 Global Macro 31 9.91 13.62 15.97 8.81 Global Macro 31 16.70 15.13 15.75 8.50 Long/Short Equity Hedge 249 16.91 8.37 14.57 7.48 Long/Short Equity Hedge 249 11.71 9.31 14.01 7.49 Long/Short Equity Hedge 249 12.36 6.98 13.64 7.35 Managed Futures 105 17.15 6.61 22.20 10.57 Managed Futures 105 21.55 15.51 22.78 11.80 Managed Futures 105 18.51 14.89 22.32 11.86 Multi Strategy 45 13.58 4.60 8.94 6.30 Multi Strategy 45 7.11 6.26 8.37 6.04 Multi Strategy 45 10.59 6.80 8.37 6.05 Fund of Funds 161 11.28 3.61 7.51 4.55 Fund of Funds 161 6.21 4.00 6.88 4.20 Fund of Funds 161 10.29 7.03 6.92 4.14
Annual Sharpe Mean 3.71 0.75 1.77 0.45 0.00 0.68 2.01 0.72 1.45 1.81 0.79 1.09 1.98 0.96 1.18 3.49 0.81 1.03 1.19 0.64 1.08 1.30 0.88 1.02 0.91 1.00 0.87 1.97 0.95 1.37 1.85 0.97 1.49
SD 5.91 0.63 0.60 0.39 0.43 0.40 1.27 0.48 0.38 1.15 0.52 0.42 0.56 0.58 0.38 4.44 0.53 0.45 0.54 0.67 0.67 0.52 0.42 0.44 0.51 0.51 0.49 0.97 0.46 0.45 0.83 0.29 0.31
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Good clone performance can be seen for convertible arbitrage (10.51% clone2 vs. 12.1% funds) and dedicated short bias (8.88% clone2 vs. 7.13% funds) where the standard deviation in mean returns is also comparable. Global macro (16.7% clone2 vs. 17.05% funds), managed futures (18.51% clone2 vs. 17.15% funds), and fund-of-funds (10.29% clone2 vs. 11.28 funds) have comparable performance in terms of average mean returns, but have much larger variation in mean returns compared to their respective funds. The other strategies offered fairly comparable performance, with the benefits of selecting the factors based on the underlying hedge fund strategy once again clearly evident across all hedge fund strategies.
5. Conclusion
This research demonstrates that selecting factors specific to the underlying hedge fund strategy has significant advantages over those constructed using a general broad set of factors for each strategy. Clone2, which used strategy-specific factors, outperformed clone1 in almost every case, and usually by a significant margin, in terms of replication performance and risk-reward ratio. Using different fund selection strategies provides investors with additional options for their hedge fund replication products.
The clones constructed using all the funds exhibited excellent replication for both the fixed and rolling window models with only a few exceptions. The benefits of selecting the factors in accordance to the hedge fund strategy were also visibly evident across all
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strategies. The top 50% Sharpe ratio funds selection strategy resulted in strong replication performance for most categories, barring fixed income arbitrage, event driven, and dedicated short bias for the fixed weight model. The rolling window model offered good replication for dedicated short bias, convertible arbitrage, managed futures, and global macro strategies. While the clone performed poorly for the other categories, there was a significant performance over the general clone1 model. The top 50% return funds selection strategy yielded clones that offered attractive replication performance for several strategies except in cases of long/short equity hedge, convertible arbitrage, event driven, and dedicate short bias for the fixed model. The rolling window model offered good clones for convertible arbitrage, dedicated short bias, global macro, managed futures, and fund-of-funds strategies. The difference in performance of hedge funds over the three fund selection procedures highlights the difficulty and importance of selecting hedge funds suitable to an investor’s preference. While there is also a difference in the performance of the clones constructed by the three clone procedures, the expense and complexity in choosing and investing in a normal hedge fund makes the clones a more favorable choice.
It is also important to recognize that costs associated with rebalancing, leveraging, and transaction costs must be considered before choosing and implementing the clones. Another point to note is that hedge funds are capable of deviating from their stated styles, and more complicated models may be needed to account for these style drifts. This is not visible when a large number of funds are averaged together, as seen in the excellent performance of clones constructed from using all funds. However, by reducing the
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number of funds considered in forming the clones, the style drift may become more apparent and difficult to capture for certain hedge fund strategies.
It is encouraging to see that using factors relevant to the hedge fund replication strategy resulted in clones that offered similar performance to the average hedge fund. The results also show that setting a higher benchmark for the clones by selecting the top performing funds continues to produce good replication performance for the clones across many strategies. The added benefits of lower fees, daily liquidity, and complete transparency make the clones appear as an attractive choice even when they slightly underperform their fund counterparts. With the view of the clones as investable products or alternatives to hedge funds, the choice in the clone construction technique depends on the desires of the investor, including clone replication performance, clone raw return, or clone riskreward performance.
References
Agarwal, Vikas, and Narayan Naik. "Multi-Period Performance Persistence Analysis of Hedge Funds." Journal of Financial and Quantitative Analysis, 35(3), 2000: 327-342. Agarwal, Vikas, and Narayan Y. Naik. "Risks and Portfolio Decisions Involving Hegde funds." The Review of Financial Studies, 17(1), 2004: 63-98.
57 Agarwal, Vikas, William Fung, Yee Cheng Loon, and Narayan Naik. "Risk and Return in Convertible Arbitrage: Evidence from the Convertible Bond Market." Journal of Empirical Finance, 18(2), 2011. Bruce, Timothy, and Kristin Reynolds. "Improving Equity Portfolio Efficiency: The Case for Long/Short Equity." NEPC, November 2010. Casano, John. "Global Macro Hegde Fund Investing: An Overview Of The Strategy." NEPC, October 2010. Credit Suisse . "An Introduction to fixed income arbitrage." Alternative Investments, March 1, 2011. Credit Suisse. "An Introduction to convertible arbitrage investing." Alternative Investments, January 31, 2011. Daniel, Edelman, William Fung, and David A. Hsieh. "Exploring Uncharted Territories of the Hedge Fund Industry: Empirical Characteristics of Mega Hedge Fund Firms." Journal of Financial Economics, 109(3), 2012. Drachman, Jordan. "Flex Ability: The Diversification Potential of Managed Futures ." Credit Suisse, April 2013. Feldman, Barry, Mary Fjelstad, and Daniel Murray. "Hedge fund replication, alternative beta and benchmarking." Russell Research, July 2009. Fung, William, and David A. Hsieh. "A Primer on Hedge Funds." Journal of Empirical Finance, 6(3), 1999: 309-331.
58 Fung, William, and David A. Hsieh. "Hedge fund benchmarks: A risk based approach." Financial Analysts Journal, 60(5), 2004: 65-80. Fung, William, and David A. Hsieh. "Hedge fund replication strategies: implications for investors and regulators." Financial Stability Review - Special issue on hedge funds, 10, 2007: 4554. Fung, William, and David A. Hsieh. "The Risk of Hedge Fund Strategies: Theory and Evidence from Trend Followers." Review of Financial Studies, 14(2), 2001: 313-341. Fung, William, and David A. Hsieh. "The Risks in Fixed-Income Hedge Fund Styles." Journal of Fixed Income, 12(2), 2002: 6-27. Fung, William, David A. Hsieh, Narayan Y. Naik, and Tarun Ramadorai. "Hedge funds: performance, risk and capital formation." Journal of Finance, 63(4), 2008: 1777-1803. Hasanhodzic, Jasmina, and Andrew W. Lo. "Can Hedge Fund Returns Be Replicated?: The Linear Case." Journal of Investment Management, 5(2), 2007: 5-45. Jaeger, Lars, and Christian Wagner. "Factor Modeling and Benchmarking of Hedge." Journal of Alternative Investments, 8(3), 2005: 9-36. Jorion, Philippe. "Risk Management Lessons From Long-Term Capital Management." European Financial Management Journal, 6(3), 2000: 277-300. Kat, Harry M., and Helder P. Palaro. "Who Needs Hedge Funds?" Cass Business school, Working paper, 27, 2005. Kugler, Peter, Jacqueline Henn-Overbeck, and Heinz Zimmermann. "Style Consistency of Hedge Fund Indexes across Providers." Applied Financial Economics, 20(5), 2010: 355-369.
59 Li, Daniel, Michael Markov, and Russ Wermers. "Monitoring Daily Hedge Fund Performance When Only Monthly Data is Available." Journal of Investment Consulting, 14(1), 2013: 57-68. Low, Jordon. "Equity Market Neutral: Diversifier Across Market Cycles." Credit Suisse, Septemeber 2009. Malkiel, Burton G., and Atanu Saha. "Hedge Funds: Risk and Return." Financial Analyst Journal, 61(6), 2005: 80-88. Sharpe, William F. "Asset Allocation: Management Style and Performance Measurement." Journal of Portfolio Management, 18, 1992: 7-19. Sourd, Véronique Le. "Hedge Fund Performance in 2008." An EDHEC Risk and Asset Management Research Centre Publication, February 2009. Suppal, Kamal, and Antolin Garza. "Assessing The Value of Multi-Strategy Fund of Hedge Funds." NEPC, September 2012. Till, Hilary, and Joseph Eagleeye. "A Hedge Fund Investor's Guide to Understanding Managed Futures ." EDHEC - Risk Institute, January 2011.
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SECTION 2. CONCLUSION
The results in the thesis show the importance of selecting factors in accordance to the economic characteristics of the underlying hedge fund when constructing replication products. The clones constructed from factors specific to each hedge fund offer good replication performance across several hedge fund categories for both fixed weight and rolling window clones when considering all funds. It was observed that these clones also continued to offer comparable performance to a higher benchmark of funds consisting of funds with higher Sharpe ratios and higher raw returns for many categories. This is a promising step forward towards the implementation of hedge fund clones, and should challenge the average hedge fund for investor capital. There are a number of points to keep in mind before selecting and implementing hedge fund replication products within one’s portfolio. First, expenses related to rebalancing within the clones, such as transaction costs and borrowing costs that are needed for the required leverage, can have a negative impact on the performance of the clones. Second, hedge funds are capable of deviating from their stated styles and more complicated models are needed to capture this style drift. Finally, hedge funds have no obligations to report their monthly performance and can stop doing so at anytime. Therefore, hedge fund databases often have missing returns. This fact, combined with the relatively short history of hedge funds, presents a challenge when developing models to create accurate clones.
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Keeping these points in mind, future research should focus on testing the validity of these results over a longer time frame and across a larger number of hedge funds. Also, to explore the possibility that fixed weight and rolling window models need different factors within the same hedge fund strategy, another possibility that needs to be analyzed is whether hedge funds have different exposures during bull markets and bear markets. Hedge fund indexes can be constructed using the various performance criteria, such as using the funds with best risk-reward ratio or the best returns, with these new indexes then being used to construct clones with the aim to replicate the constructed index. The research in this thesis establishes the importance of using factors relevant to the underlying hedge fund strategy in the replication process and offers investors the choice between clone replication performance, clone raw return, and clone risk-reward performance. The success of hedge fund replication products will rely on the ability of the clones to offer the benefits traditionally expected from hedge funds, such as offering protection and diversity in an investors’ portfolio, while hopefully generating above average returns. It is an exciting time in the world of hedge fund replication and there is reason to be optimistic that hedge fund-like returns can be achieved without investing directly in more expensive hedge funds.
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VITA
Sujit Subhash was born in Trichur, India on October 6, 1988. He received his B.E. in Mechanical Engineering from M.S. Ramaiah Institute of Technology in June, 2010. He worked as a Project Assistant at the Indian Institute of Science between March, 2011 and July, 2012. He joined Missouri University of Science and Technology as a graduate student in the Engineering Management and Systems Engineering Department in August, 2012. In April, 2014, he was awarded the 2013-2014 Outstanding MS Graduate Student Research Award from the Engineering Management and Systems Engineering Department at Missouri University of Science and Technology. In December, 2014, he received his M.S. in Engineering Management from Missouri University of Science and Technology, Rolla, Missouri.
